Simplify the following expression and state the condition under which the simplification is valid. $n = \dfrac{r^2 - 16}{r + 4}$
Explanation: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = r$ $ b = \sqrt{16} = 4$ So we can rewrite the expression as: $n = \dfrac{({r} + {4})({r} {-4})} {r + 4} $ We can divide the numerator and denominator by $(r + 4)$ on condition that $r \neq -4$ Therefore $n = r - 4; r \neq -4$